#############################################################################
##
#F                             CHEVIE library
##
#Y  Copyright 1992--1994,  Lehrstuhl D f"ur Mathematik,    RWTH Aachen,   and
#Y                         IWR   der   Universit"at    Heidelberg,   Germany.
##
#############################################################################

olprint(`**********************************************************************\
****`);
olprint(`*                                                                     \
   *`);
olprint(`*                                                                     \
   *`);
olprint(`*                    Unipotent characters of GU_4(q)                  \
   *`);
olprint(`*                                                                     \
   *`);
olprint(`*                                                                     \
   *`);
olprint(`**********************************************************************\
****`);
`uniGU4`   :=array(-2..5,-1..23,[
[`GU_4(q)`,`uni2A3002`
,   q^6*(q^2+1)*(q^2-q+1)*(q-1)^2*(q+1)^4
,   5
,   5
,   23
,   23
]
,[
``,``,
[`^2A_3(q)`,   q+1   ,   [[1, 1, 1, 1]]   ]
,
[`^2A_3(q)`,   q+1   ,   [[2, 1, 1]]   ]
,
[`^2A_3(q)`,   q+1   ,   [[2, 2]]   ]
,
[`^2A_3(q)`,   q+1   ,   [[3, 1]]   ]
,
[`^2A_3(q)`,   q+1   ,   [[4]]   ]
,
[`^2A_2(q)`,   (q+1)^2   ,   [[1, 1, 1]]   ]
,
[`^2A_2(q)`,   (q+1)^2   ,   [[2, 1]]   ]
,
[`^2A_2(q)`,   (q+1)^2   ,   [[3]]   ]
,
[`A_1(q)+A_1(q)`,   (q+1)^2   ,   [[1, 1], [1, 1]]   ]
,
[`A_1(q)+A_1(q)`,   (q+1)^2   ,   [[1, 1], [2]]   ]
,
[`A_1(q)+A_1(q)`,   (q+1)^2   ,   [[2], [1, 1]]   ]
,
[`A_1(q)+A_1(q)`,   (q+1)^2   ,   [[2], [2]]   ]
,
[`A_1(q^2)`,   (q-1)*(q+1)   ,   [[1, 1]]   ]
,
[`A_1(q^2)`,   (q-1)*(q+1)   ,   [[2]]   ]
,
[`A_1(q)`,   (q+1)^3   ,   [[1, 1]]   ]
,
[`A_1(q)`,   (q+1)^3   ,   [[2]]   ]
,
[`A_1(q)`,   (q-1)*(q+1)^2   ,   [[1, 1]]   ]
,
[`A_1(q)`,   (q-1)*(q+1)^2   ,   [[2]]   ]
,
[`\\emptyset`,   (q+1)^4   ,   [[[1]], 1]   ]
,
[`\\emptyset`,   (q-1)*(q+1)^3   ,   [[[1]], 1]   ]
,
[`\\emptyset`,   (q-1)^2*(q+1)^2   ,   [[[1]], 1]   ]
,
[`\\emptyset`,   (q^2-q+1)*(q+1)^2   ,   [[[1]], 1]   ]
,
[`\\emptyset`,   (q-1)*(q+1)*(q^2+1)   ,   [[[1]], 1]   ]
]
,[
erg[0,-1]   ,
erg[0,0]   ,
1   ,
q^6-q^5+q^4-q^2+q-1   ,
q^8+q^5-q^4-q   ,
q^10-q^9+q^7-2*q^6+q^5-q^3+q^2   ,
q^12-q^10+q^9-q^8-q^7+q^6-q^5+q^3   ,
(q-1)*(q^2+1)*q^3   ,
(q^4-q^3+q-1)*(q-1)*(q^2+1)*q^3   ,
(q^6-q^4+q^3-q)*(q-1)*(q^2+1)*q^3   ,
(q^2+1)*(q^2-q+1)*q^4   ,
(q^2-1)*(q^2+1)*(q^2-q+1)*q^4   ,
(q^2-1)*(q^2+1)*(q^2-q+1)*q^4   ,
(q^4-2*q^2+1)*(q^2+1)*(q^2-q+1)*q^4   ,
(q^2-q+1)*(q+1)^2*q^4   ,
(q^4-1)*(q^2-q+1)*(q+1)^2*q^4   ,
(q-1)*(q^2+1)*(q^2-q+1)*q^5   ,
(q^2-1)*(q-1)*(q^2+1)*(q^2-q+1)*q^5   ,
(q+1)*(q^2+1)*(q^2-q+1)*q^5   ,
(q^2-1)*(q+1)*(q^2+1)*(q^2-q+1)*q^5   ,
(q^2+1)*(q^2-q+1)*(q-1)^2*q^6   ,
(q-1)*(q+1)*(q^2+1)*(q^2-q+1)*q^6   ,
(q^2+1)*(q^2-q+1)*(q+1)^2*q^6   ,
(q^2+1)*(q-1)^2*(q+1)^2*q^6   ,
(q-1)*(q^2-q+1)*(q+1)^3*q^6   ]
,[
[[1, 1, 1, 1]]   ,
q^6   ,
q^6   ,
0   ,
0   ,
0   ,
0   ,
-q^3   ,
0   ,
0   ,
q^2   ,
0   ,
0   ,
0   ,
q^2   ,
0   ,
-q   ,
0   ,
q   ,
0   ,
1   ,
-1   ,
1   ,
1   ,
-1   ]
,[
[[2, 1, 1]]   ,
(q^2-q+1)*q^3   ,
(q^2-q+1)*q^3   ,
q^3   ,
0   ,
0   ,
0   ,
q*(q^2-q+1)   ,
q   ,
0   ,
-q*(q-2)   ,
q   ,
q   ,
0   ,
q^2   ,
0   ,
2*q-1   ,
-1   ,
1   ,
1   ,
-3   ,
1   ,
1   ,
0   ,
-1   ]
,[
[[2, 2]]   ,
q^2*(q^2+1)   ,
q^2*(q^2+1)   ,
q^2   ,
q^2   ,
0   ,
0   ,
(q-1)*q   ,
-q   ,
0   ,
q^2+1   ,
1   ,
1   ,
1   ,
q^2+1   ,
1   ,
-q+1   ,
1   ,
q+1   ,
1   ,
2   ,
0   ,
2   ,
-1   ,
0   ]
,[
[[3, 1]]   ,
q*(q^2-q+1)   ,
q*(q^2-q+1)   ,
-(q-1)*q   ,
q   ,
q   ,
0   ,
-q^2+q-1   ,
q-1   ,
-1   ,
2*q-1   ,
q-1   ,
q-1   ,
-1   ,
1   ,
1   ,
q-2   ,
-2   ,
q   ,
0   ,
-3   ,
-1   ,
1   ,
0   ,
1   ]
,[
[[4]]   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ]
]):
KlassentypOrduni2A3002:=   [q+1, q+1, q+1, q+1, q+1, q^2+q, q^2+q, q^2+q, 1/2*q
^2+1/2*q, 1/2*q^2+1/2*q, 1/2*q^2+1/2*q, 1/2*q^2+1/2*q, 1/2*q^2-1/2*q-1, 1/2*q^2
-1/2*q-1, 1/2*q^3-1/2*q, 1/2*q^3-1/2*q, 1/2*q^3-3/2*q-1, 1/2*q^3-3/2*q-1, 1/24*
q^4-1/12*q^3-1/24*q^2+1/12*q, 1/4*q^4-3/4*q^2-1/2*q, 1/8*q^4-1/4*q^3-5/8*q^2+3/
4*q+1, 1/3*q^4+1/3*q^3-1/3*q^2-1/3*q, 1/4*q^4-1/4*q^2]   :
NurPolynomuni2A3002:=true:
Informationuni2A3002:=TEXT(
`- Information about the tables of unipotent characters for GU_4(q).`,
``,
`- CHEVIE-name of the table: uniGU4`,
``,
`- This table is computed with general programs written by F.Luebeck.`,
`  They compute the Deligne-Lusztig characters R_T^G(1) and find the`,
`  unipotent characters as linear combinations of them.`,
``):

g:=`uniGU4`:
print(` g := ``uniGU4`` `);
